Shaken staples stick together

All experimental physicists know that some tasks can be tedious and painstaking, but Nick Gravish from the Georgia Institute of Technology has just taken this to a new level. In a series of experiments to find out more about the behaviour of U-shaped objects, Gravish and colleagues spent about 10 man-hours carefully trimming the arms of thousands of steel staples to see how their shape affects how the staples cling together.

To their surprise, the researchers found that there is an optimum arm length, above and below which the staples are less likely to stick together when shaken. As well as helping scientists to understand materials that are made of U-shaped components, the research could also provide insight into how biological systems as diverse as fire-ant rafts and eagle nests are formed.

Humble but complex

Physicists have a long history of studying the behaviour of granular materials, for example to find out why sand piles collapse or why grains jam when passing through an industrial "hopper". Some granular materials – including some colloids – can even become entangled with each other and so behave very differently from particles with simple shapes, such as sand grains.

Humble staples are an ideal way of gaining a better understanding of how this entanglement occurs because they are a very simple example of an object that can mechanically grab hold of its neighbours. Carried out by Gravish, Dan Goldman and David Hu at Georgia Tech along with Scott Franklin at the Rochester Institute of Technology, each experiment began with a clump of staples all with the same arm length. The researchers placed the staples in a cylindrical mould that is on top of a vibrating plate. After vibrating the column of staples for about 20 s to ensure that it is in a tightly packed state, the team found that the density of the column was greatest for staples with no arms – essentially rods – and that the density dropped off for staples with longer arms.

The researchers then removed the cylinder before shaking the free-standing column again and monitoring it with a digital camera. As the column collapsed, they measured its height as a function of time, from which they derived the average energy required to disentangle one staple from another.

Long arms

As expected, this "energy barrier" rises as the arm length increases because a staple with a longer arm takes more energy to disentangle. What was surprising, however, was that the energy barrier did not keep on rising, but rather peaked in staples where the arms are about 40% of the width of the staple. For longer arms, the energy appeared to drop off.

When Gravish and colleagues carried out computer simulations of how the staples pack and collapse, they found that another factor was at work. It turns out that in the case of staples with arms longer than about 40% of their width, these objects do not pack as tightly as their shorter counterparts. The result is that there is less entanglement in the column to begin with and so it takes less energy to shake it apart.

While the team's work should provide clues to the behaviour of materials made of entangled inanimate objects such as some colloids, Gravish and Goldman say that it cannot fully explain how living organisms such as fire ants hook themselves together into structures such as floating mats – which are made to save an entire ant colony in a flood. Instead, they believe that the work will allow biologists to differentiate between purely mechanical effects and behavioural effects that define how such structures are made.

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9 comments

Any magnetic effects?

Interesting. One assumes that the entanglement is purely mechanical due to the hooking action of the arms of the staples with others. Have the researchers tested for any trace magnetic effects before and after the shaking, that might have influenced the results?

Limited relevance

It is quite interesting to see the resistence-barrier to collapse of the aggregate of the entangled U-staples passes through a maximum as a function of the ratio of the arm-length to its width. However, this works's relevance to the triggering of an avanlanche, the collapsing of a sand dune and the forming of floating mats by the fire ants, is doubtful

Starting vibrational force

Vladimir, interesting thought. However, one may check it out by making the entangled staples practically armless (compared to their width) In this case the geometrical induction influence should be practically absent and the agregate should collapse without much vibrating force. If it does not collapse due to some,say, residual magnetic effect, one can determine the vibrating force needed to demolish the agregate. Thereafter, this force should be the starting point for studying the geometric entanglement factor in its differnt phases. In a way this additional force, may be taken as a necessary "background on which the real signal comes up.

A variant

(common observation) Put a number of leads together in a box, and very quickly they interwine promiscuously together, making it difficult to extract the one you want. There's a good research project for someone, though maybe polymer physicists have already sorted this one out.

Leads to connecting cables

Brian, I do not know the solution to your promiscuously interwined-leads-in-a-box problem. Of course, you cannot shake them out their even-unintended promiscuity! However, you have a bit similar problem, when you work with a large number of connecting cables in an experiment. The best way to reduce the interwining complexity seems to be to make them as short as possible.Brian, allow me a small diversion here: Will you use the same "Charge Josephson Effect" equations to treat the dynamics of the "magnetic Josephson Effect" discoverd recently? I shall appreciate a word on it.

(common observation) Put a number of leads together in a box, and very quickly they interwine promiscuously together, making it difficult to extract the one you want. There's a good research project for someone, though maybe polymer physicists have already sorted this one out.

Vladimir, interesting thought. However, one may check it out by making the entangled staples practically armless (compared to their width) In this case the geometrical induction influence should be practically absent and the agregate should collapse without much vibrating force. If it does not collapse due to some,say, residual magnetic effect, one can determine the vibrating force needed to demolish the agregate. Thereafter, this force should be the starting point for studying the geometric entanglement factor in its differnt phases. In a way this additional force, may be taken as a necessary "background on which the real signal comes up.

Or use different material

Vladimir, interesting thought. However, one may check it out by making the entangled staples practically armless (compared to their width) In this case the geometrical induction influence should be practically absent and the agregate should collapse without much vibrating force. If it does not collapse due to some,say, residual magnetic effect, one can determine the vibrating force needed to demolish the agregate. Thereafter, this force should be the starting point for studying the geometric entanglement factor in its differnt phases. In a way this additional force, may be taken as a necessary "background on which the real signal comes up.

Seems to me that if you repeat the experiment with, say, plastic staples of the same dimensions, you should see the same effect, and perhaps be able to separate the strictly mathematical component of the entanglement from, say, the energy needed to overcome the inertia and weight of the objects.

A new construction material?

This reminds me of the game pick-up-sticks where one tries to withdraw a stick from an intertwined pile without moving any other. Two questions - is the staple shape the most efficient for the strongest linkage? I doubt it. And would such units poured (and shaken) into a thin cardboard box or mold to preserve the overall shape shape be strong enough for a sort of lightweight construction material? Quote:

(common observation) Put a number of leads together in a box, and very quickly they interwine promiscuously together, making it difficult to extract the one you want. There's a good research project for someone, though maybe polymer physicists have already sorted this one out.

Shaken staples stick together.

Of course staples would stick, or at least entwine each other. And be more of a challenge to disentangle as the container allows fewer directions for removal. But that does not relate to sand or other particulates sticking in a hopper. That is controlled by the intergranular friction and the vertical-to-horizontal movement in the hopper. The effect is analogous to building an arch out of blocks. These effects, as well as the ratios of static to dynamic friction, explain the collapse of sand walls in excavations.